Unsupervised multivariate time series trend detection for group behavior analysis

ABSTRACT

A method for unsupervised multivariate time series trend detection for group behavior analysis is presented. The method includes collecting multi-variate time series data from a plurality of sensors, learning piecewise linear trends jointly for all of the multi-variate time series data, dividing the multi-variate time series data into a plurality of time segments, counting a number of up/down trends in each of the plurality of time segments, for a training phase, employing a cumulative sum (CUSUM), and, for a testing phase, monitoring the CUSUM for trend changes.

RELATED APPLICATION INFORMATION

This application claims priority to Provisional Application No.62/892,095, filed on Aug. 27, 2019, and Provisional Application No.62/892,615, filed on Aug. 28, 2019, the contents of which areincorporated herein by reference in their entirety.

BACKGROUND Technical Field

The present invention relates to trends in time series data and, moreparticularly, to methods and systems for unsupervised multivariate timeseries trend detection for group behavior analysis and tensorized longshort-term memory (LSTM) with adaptive shared memory for learning trendsin multivariate time series.

Description of the Related Art

A large amount of time series data has been generated from variousdomains, such as traffic management, electricity consumption andalgorithmic trading. Trend learning in time series data aims to analyzethe evolving trends in time series and forecast the trend. Trendlearning is attractive because it can deliver more information about thesemantics and dynamics of the underlying process generating the timeseries compared to conventional prediction methodologies. There has beena lot of effort on learning trends in time series data.

SUMMARY

A computer-implemented method for unsupervised multivariate time seriestrend detection for group behavior analysis is presented. The methodincludes collecting multi-variate time series data from a plurality ofsensors, learning piecewise linear trends jointly for all of themulti-variate time series data, dividing the multi-variate time seriesdata into a plurality of time segments, counting a number of up/downtrends in each of the plurality of time segments, for a training phase,employing a cumulative sum (CUSUM), and, for a testing phase, monitoringthe CUSUM for trend changes.

A non-transitory computer-readable storage medium comprising acomputer-readable program is presented for unsupervised multivariatetime series trend detection for group behavior analysis, wherein thecomputer-readable program when executed on a computer causes thecomputer to perform the steps of collecting multi-variate time seriesdata from a plurality of sensors, learning piecewise linear trendsjointly for all of the multi-variate time series data, dividing themulti-variate time series data into a plurality of time segments,counting a number of up/down trends in each of the plurality of timesegments, for a training phase, employing a cumulative sum (CUSUM), and,for a testing phase, monitoring the CUSUM for trend changes.

A system for unsupervised multivariate time series trend detection forgroup behavior analysis is presented. The system includes a memory andone or more processors in communication with the memory configured tocollect multi-variate time series data from a plurality of sensors,learn piecewise linear trends jointly for all of the multi-variate timeseries data, divide the multi-variate time series data into a pluralityof time segments, count a number of up/down trends in each of theplurality of time segments, for a training phase, employ a cumulativesum (CUSUM), and, for a testing phase, monitor the CUSUM for trendchanges.

A computer-implemented method for executing a multi-task deep learningmodel for learning trends in multivariate time series is presented. Themethod includes collecting multi-variate time series data from aplurality of sensors, jointly learning both local and global contextualfeatures for predicting a trend of the multivariate time series byemploying a tensorized long short-term memory (LSTM) with adaptiveshared memory (TLASM) to learn historical dependency of historicaltrends, and employing a multi-task one-dimensional convolutional neuralnetwork (1dCNN) to extract salient features from local raw time seriesdata to model a short-term dependency between local time series data andsubsequent trends.

A non-transitory computer-readable storage medium comprising acomputer-readable program is presented for executing a multi-task deeplearning model for learning trends in multivariate time series, whereinthe computer-readable program when executed on a computer causes thecomputer to perform the steps of collecting multi-variate time seriesdata from a plurality of sensors, jointly learning both local and globalcontextual features for predicting a trend of the multivariate timeseries by employing a tensorized long short-term memory (LSTM) withadaptive shared memory (TLASM) to learn historical dependency ofhistorical trends, and employing a multi-task one-dimensionalconvolutional neural network (1dCNN) to extract salient features fromlocal raw time series data to model a short-term dependency betweenlocal time series data and subsequent trends.

A system for executing a multi-task deep learning model for learningtrends in multivariate time series is presented. The system includes amemory and one or more processors in communication with the memoryconfigured to collect multi-variate time series data from a plurality ofsensors, jointly learn both local and global contextual features forpredicting a trend of the multivariate time series by employing atensorized long short-term memory (LSTM) with adaptive shared memory(TLASM) to learn historical dependency of historical trends, and employa multi-task one-dimensional convolutional neural network (1dCNN) toextract salient features from local raw time series data to model ashort-term dependency between local time series data and subsequenttrends.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a block/flow diagram of a method for unsupervised multivariatetime series trend detection for group behavior analysis, in accordancewith embodiments of the present invention;

FIG. 2 are block/flow diagrams of joint piecewise linear trends learningand trend segment breaking, in accordance with embodiments of thepresent invention;

FIG. 3 are block/flow diagrams of count up/down trend numbers in eachtrend time segment, CUSUM training, and CUSUM monitoring for changedetection, in accordance with embodiments of the present invention;

FIG. 4 is a block/flow diagram of trend prediction in multivariate timeseries, in accordance with embodiments of the present invention;

FIG. 5 is block/flow diagram of a basic multi-task learning (MTL)setting, in accordance with embodiments of the present invention;

FIG. 6 is block/flow diagram of an enhanced multi-task learning (MTL)setting, in accordance with embodiments of the present invention;

FIGS. 7-8 are block/flow diagrams of an architecture of the tensorizedLSTM with adaptive shared memory (TLASM) for modeling temporal patternsof two time series, in accordance with embodiments of the presentinvention;

FIG. 9 is block/flow diagram of an exemplary processing system forunsupervised multivariate time series trend detection for group behavioranalysis, in accordance with embodiments of the present invention;

FIG. 10 is a block/flow diagram of an exemplary method for unsupervisedmultivariate time series trend detection for group behavior analysis, inaccordance with embodiments of the present invention;

FIG. 11 is a block/flow diagram of equations employed in an exemplarymethod for unsupervised multivariate time series trend detection forgroup behavior analysis, in accordance with embodiments of the presentinvention;

FIG. 12 is a block/flow diagram of practical applications forunsupervised multivariate time series trend detection for group behavioranalysis, in accordance with embodiments of the present invention;

FIG. 13 is a block/flow diagram of method for tensorized LSTM withadaptive shared memory for learning trends in multivariate time series,in accordance with embodiments of the present invention;

FIG. 14 are block/flow diagrams of training the TLASM model andpredicting future trend's slope and length, in accordance withembodiments of the present invention;

FIG. 15 is a block/flow diagram of exemplary IoT sensors used to collectdata/information for unsupervised multivariate time series trenddetection for group behavior analysis, in accordance with embodiments ofthe present invention; and

FIG. 16 is a block/flow diagram of an exemplary method for tensorizedLSTM with adaptive shared memory for learning trends in multivariatetime series, in accordance with embodiments of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In many real-world applications, time series data is in the form ofmultivariate. Hence, trend learning is further extended to multivariatetime series data. Trend learning in multivariate time series isdifficult because of complex temporal patterns hidden in themultivariate time series, especially the existence of dependencies amongthe time series in the group. In many applications, the time series in agroup share similar trend patterns. For example, traffic congestion thathappens on a road causes all vehicles on the road to slow down. Thus,the number and the average speed of cars slowing down in a road segmentare the indicator of possible traffic congestion. Another examplerelates to complex system monitoring. In a cyber-physical system,sensors are deployed to monitor each device and record time series data.When the number of increasing (uptrend) or decreasing (down-trend) timeseries in a subsystem is increasing, there should be some system anomalyin that subsystem.

In one example of single time series trend detection, the exemplaryembodiments detect a trend in each time period. For each local trend,exemplary embodiments need to detect a time length and a slope. Theexemplary embodiments can have threshold on length and slope to maintainonly a subset of trends. The multivariate time series in the same group,e.g., stocks in the same sector or vehicle speed in the same roadsegment during a period time, usually has similar trend patterns. Thechallenge is how to detect the trend of the group as a wholecharacteristic for group behavior analysis.

To address such issue, the exemplary embodiments use an l₁ trendfiltering method on the whole multi-variate time series. The exemplaryembodiments learn the piecewise linear trends for all the time seriesjointly using the following equation:

∑ t = 1 T    y ^ t - x ^ t  2 2 + λ  ∑ t = 2 T - 1    x ^ t -1 - 2  x ^ t + x ^ t + 1  2 , where   y ^ t , x ^ t ∈ k

Here, y_(t) is the original multi-variate time series values at timestep t, which is a k-dimensional vector (R^(k×1)). x_(t) (t=1 to T) isthe estimated value to be optimized. The first term of the aboveequation is the residual term and the second term is the smoothnessterm. λ is used to control the granularity of the inferred trends.Basically, if λ is larger, the resulting trend would be coarse grained.

After the optimization, the exemplary embodiments use the estimatedx_(t) to break the multivariate time series into different segments asshown in the following steps, pseudo code:

  for t = 1 to T − 2  for i = 1 to k  if ∥ {circumflex over (x)}_(t+2)(i)−2 {circumflex over (x)}_(t+1) (i)+ {circumflex over (x)}_(t) (i)∥₂ > ϵ   Break time series at t + 1;   break;

Once the exemplary embodiments break the optimized x_(t) into piece-wiselinear trend segments, the method can further count the number ofup/down trends in each time segment. The resulting counts time seriesdescribe the trend evolution of the whole multi-variate time series.

The exemplary embodiments denote the number of uptrends as z_(n)(1≤n≤N). N is the total number of trend segments. This is similar forthe downtrend cases. The exemplary embodiments can then use cumulativesum (CUSUM) to monitor the group of time series (multi-variate timeseries) trends. When the cumulative sum of deviations is larger thansome threshold θ, the exemplary embodiments report that the group oftime series has an increasing uptrend. If the CUSUM value is less thanθ, the method reports that the group has a decreasing uptrend.

The equation of calculating CUSUM is as follows:

$S_{n} = {\sum\limits_{i = 1}^{n}\; {\left( {z_{n} - \mu} \right)\text{/}\sigma_{z}}}$

Here, μ is the mean value of z in the training period, σ_(z) is thestandard error of z in the training period.

FIG. 1 is a block/flow diagram of a method for unsupervised multivariatetime series trend detection for group behavior analysis, in accordancewith embodiments of the present invention.

At block 101, a multi-variate time series is input.

At block 103, joint piecewise linear trends are learned.

At block 105, trend segment breaking (or dividing) is determined.

At block 107, the trend numbers in each trend time segment are countedup/down.

At block 109, for the training phase, cumulative sum (CUSUM) training isperformed.

At block 111, for the testing phase, CUSUM monitoring for changedetection is performed.

FIG. 2 are block/flow diagrams of joint piecewise linear trends learningand trend segment breaking, in accordance with embodiments of thepresent invention.

At block 103, joint piecewise linear trends are learned.

At block 201, formula (1) is employed to learn optimized x.

At block 203, λ is used to control the granularity of the inferredtrends. The selection of λ depends on users' application requirements.If the user is interested in a short-term trend, λ can be small.

At block 105, trend segment breaking (or dividing) is determined.

At block 211, algorithm (1) is used to break the trend time segments.

At block 213, ε is used to control the granularity, and usually a smallvalue is sufficient, e.g., 10⁻³.

FIG. 3 are block/flow diagrams of count up/down trend numbers in eachtrend time segment, CUSUM training, and CUSUM monitoring for changedetection, in accordance with embodiments of the present invention.

At block 107, the trend numbers in each trend time segment are countedup/down.

At block 221, it is possible to apply thresholds on trends, say a lengthand a slope.

At block 109, for the training phase, cumulative sum (CUSUM) training isperformed.

At block 231, the mean and standard deviation (μ and σ_(z)) arecalculated for the training data. The training data are historicaltrends.

At block 111, for the testing phase, CUSUM monitoring for changedetection is performed.

At block 241, formula (2) is employed to calculate S_(n). If it arrivesat some threshold, the system triggers a changing alert.

Therefore, regarding unsupervised multivariate time series trenddetection for group behavior analysis, trends in multivariate timeseries characterize the movement of time series. Learning andforecasting time series movements is invaluable to various real-worldapplications, such as traffic management, electricity consumption, andalgorithmic trading. Given the historical data of each time series, theexemplary embodiments aim to forecast the slope and duration of thesubsequent trend of each time series. This task is challenging becauseof the complex temporal patterns of multivariate time series and theuncertainty in the relations between different time series.

The exemplary embodiments below introduce a novel deep neural networkmodel, namely tensorized LSTM with adaptive shared memory (TLASM), toresolve such challenges. TLASM employs the tensorized LSTM in which thehidden states are represented by tensors to model the temporal patternsof multivariate time series trends. With an adaptive shared memory,TLASM is able to learn the relation between time series adaptively. Thetensorized LSTM helps TLASM enjoy the advantage of multi-task learningin which the trend learning of each time series is considered as a task.The adaptive shared memory makes the more related tasks share more modelparameters. Furthermore, with the tensorized LSTM applied to time seriestrends and the one-dimensional convolutional neural network (1dCNN)applied to local time series data, the long-term dependency within thesequence of historical trends and the short-term dependency between thelocal raw time series data and the subsequent trend are considered.

The problem of learning and forecasting underlying trends in time seriesdata arises in a variety of applications, such as traffic management,energy optimization, etc. A trend in time series is characterized by theslope and duration, and its prediction is then to forecast the twovalues of the subsequent trend given historical data of the time series.For this problem, existing approaches mainly deal with the case inunivariate time series.

However, in many real-world applications, there are multiple variablesat play, and handling all of them at the same time is beneficial for anaccurate prediction. A natural way is to employ multi-task learning(MTL) techniques in which the trend learning of each time series istreated as a task. The key point of MTL is to learn task relatedness toachieve better parameter sharing, which however is challenging in trendprediction tasks. First, effectively modeling the complex temporalpatterns in different tasks is difficult as the temporal and spatialdimensions are entangled. Second, the relatedness among tasks may changeover time.

The exemplary embodiments address such issues by introducing a neuralnetwork, referred to as DeepTrends, for multivariate time series trendprediction. The core module of DeepTrends is a tensorized LSTM withadaptive shared memory (TLASM). TLASM employs the tensorized LSTM tomodel the temporal patterns of long-term trend sequences in an MTLsetting. With an adaptive shared memory, TLASM is able to learn therelatedness among tasks adaptively, based upon which TLASM candynamically vary degrees of parameter sharing among tasks. To furtherconsider short-term patterns, DeepTrends utilizes a multi-task 1dCNN tolearn the local time series features and employs a task-specificsub-network to learn a mixture of long-term and short-term patterns fortrend prediction.

In the MTL setting, the trend learning of each time series is consideredas a task and different tasks are performed jointly. MTL can helpimprove the performance of tasks when they are related, and MTL alsosaves the computation cost by sharing model architectures (parameters)between related tasks. However, the MTL model may suffer significantdegeneration in performance when tasks are less related to each other.

FIG. 5 illustrates a basic MTL model 500 for modeling the temporalpatterns of two time series, where each time series has its ownparameters to generate hidden representations and the hiddenrepresentations of different time series influence each other byadditional shared parameters. Compared to models without parametersharing, the basic MTL model introduces inductive bias into the sharedarchitecture. When tasks are unrelated, the inductive biases indifferent tasks will have conflicts and hurt task performance. Toalleviate this problem, a memory enhanced model that decouples thehidden representations into the task specific patterns and the sharedones can be employed. The architecture of the enhanced MTL 600 is shownin FIG. 6, in which an external memory is designed to share informationamong different tasks. However, the shared memory cannot model taskrelatedness for better parameter-sharing. Another challenge comes fromthe temporal dynamics in different tasks. In many cases, the relatednessamong tasks may change over time. However, FIG. 4 can be employed toalleviate issues related to the basic MTL 500 and the enhanced MTL 600.

FIG. 4 is a block/flow diagram of trend prediction in multivariate timeseries, in accordance with embodiments of the present invention.

To address the above challenges, the exemplary embodiments introduce adeep architecture, referred to as DeepTrends 400, for learning trends inmultivariate time series as shown in FIG. 4. DeepTrends jointly learnsboth local and global contextual features for predicting the trend oftime series. DeepTrends core module is a tensorized LSTM with adaptiveshared memory (TLASM 401) to learn the sequential dependency ofhistorical trends, which carries the information about long-term trendevolving. To further consider short-term dependency, DeepTrends utilizesa multitask 1dCNN 403 to learn the features of local raw time series,which delivers the information about the abrupt changing behavior of thetrend evolution.

Specifically, TLASM 401 leverages the tensorized LSTM to model thecomplex temporal patterns in different tasks, based upon which, anadaptive shared memory is designed to learn the task relatedness anddynamically integrate the shared information from related tasks into therepresentation of each individual task. The adaptive shared memoryincludes multiple layers of sub-networks. TLASM 401 learns thesub-network connections between different layers for informationrouting. In this way, one learning task can share more parameters withmore related ones by selecting a similar sub-network. Each task isassociated with one task specific unit at each time step for dynamicalinformation routing. The idea of sub-network routing has not beenpreviously used for the sequential model. Moreover, time series dataoften involves a mixture of long-term and short-term patterns. InDeepTrends, TLASM 401 is employed to model the long-term dependencywithin the sequence of historical trends. Since CNN is good atextracting patterns of local salience by applying a local connectivitybetween neurons, DeepTrends further employs a multi-task 1dCNN 403 toextract salient features from local raw time series data, so as to modelthe short-term dependency between local time series data and thesubsequent trend. A task-specific sub-network is then designed tointegrate the long- and short-term dependency.

The advantages of the present application can be summarized as follows:

The exemplary embodiments present DeepTrends, a multi-task deep learningmodel for learning trends in multivariate time series, which considersboth long- and short-term dependency.

The exemplary embodiments introduce TLASM, which is the first neuralnetwork capable to jointly model the temporal patterns of multivariatetime series and achieve flexible parameter sharing.

The exemplary embodiments extend the problem setting into a multivariateone. n time series is denoted by X=(x¹, . . . , x^(n))^(T)=(x₁, . . . ,x_(T))∈

^(n×T), where =(x₁ ^(i), . . . , x_(T) ^(i))^(T)∈

^(T) is the i-th time series and x_(t)=(x_(t) ^(t), . . . , x_(t)^(n))^(T)∈

^(T) represents the vector of n time series at time step t. T is thenumber of time steps. The historical trend sequence of λ is the union ofthe trend sequence over each time series and denoted by

={

l_(k) ¹,s_(k) ¹

}∪ . . . ∪{

l_(k) ^(n),s_(k) ^(n)

}, where {

l_(k) ^(i),s_(k) ^(i)

} is the trend sequence of the i-th time series.

l_(k) ^(n),s_(k) ^(i)

is the k-th trend of the i-th time series and describes a function overa subsequence (or a segment) of the i-th time series. l_(k) ^(i) ands_(k) ^(i) represent the duration and slope of the k-th trend in thei-th time series respectively. l_(k) ^(i) is measured in terms of thetime range covered by the k-th trend of the i-th time series. Both l_(k)^(i) and s_(k) ^(i) are continuous values. Trends of X are time orderedand non-overlapping. The durations of all the trends in each time seriesaddress Σ_(k)l_(k) ^(i)=T.

The local time series data delivers the information about the abruptchanging behavior of the trend evolution. The local data with respect toeach historical trend is defined as the time series data with windowsize w.

The local data of X is denoted by:

={

x_(t) _(k) _(−w) ¹, . . . , x_(t) _(k) ¹

}∪ . . . ∪{

x_(t) _(k) _(−w) ^(n), . . . , x_(t) _(k) ^(n)

}, where

x_(t) _(k) _(−w) ^(i), . . . , x_(t) _(k) ^(i)

is the local data of the k-th trend of the i-th time series and t_(k) isthe ending time of the k-th trend. Given

and

, the goal is to learn the trends in multivariate time series forforecasting the subsequent trend of each time series, e.g.,

{circumflex over (l)}¹,ŝ¹

, . . .

{circumflex over (l)}^(n),ŝ^(n)

.

Data instances are built by combining the historical trend sequence,local raw time series data and the subsequent trends. All data instancesare split into training set (80%), validation set (10%) and test set(10%). To generate trends, the exemplary embodiments adopt the l₁ trendfiltering for multivariate time series.

The objective function is:

${\sum\limits_{t = 1}^{T}\; {{{\hat{y}}_{t} - {\hat{x}}_{t}}}_{2}^{2}} + {\mu {\sum\limits_{t = 2}^{T - 1}\; {{{\hat{x}}_{t - 1} - {2{\hat{x}}_{t}} + {\hat{x}}_{t + 1}}}_{2}}}$

where x_(t)∈

^(n) is the time series data at time step t and {circumflex over(x)}_(t) is the estimate.

Using a similar idea in the group Lasso, the objective function couplestogether changes in the slopes of individual entries at the same timeindex, so the trend component found tends to show simultaneous trendchanges. It is noted that even though the trends in multivariate timeseries are asynchronous, the trend is split into smaller pieces andmaintains the predictive power. In the objective function, μ is aparameter to control the number of generated trends. The smaller μ is,the more fine-grained the trends are. The specific value of μ depends onthe user's need.

The exemplary embodiments first introduce the basic LSTM, followed byhow to extend it into the tensorized one with adaptive shared memory.

The LSTM network is a powerful approach to learn the long-termdependency of sequential data. The calculation process of the LSTM unit(applied to each time step) is described with respect to the equationsbelow.

Given a sequence of input data x₁, x₂, . . . ∈

^(n), a memory cell c_(t)∈

^(d) and a hidden state h_(t)∈

^(d) are calculated for each input data by the following equations:

${\begin{bmatrix}c_{t} \\f_{t} \\i_{t} \\o_{t}\end{bmatrix} = {\begin{bmatrix}\tanh \\\sigma \\\sigma \\\sigma\end{bmatrix}\left( {{W\left\lbrack {x_{t} \oplus h_{t - 1}} \right\rbrack} + b} \right)}},{c_{t} = {{f_{t} \odot c_{t - 1}} + {i_{t} \odot {\overset{\sim}{c}}_{t}}}},{h_{t} = {o_{t} \odot {\tanh \left( c_{t} \right)}}},$

where W∈

^(4d×(N+d)) and b∈R^(4d) are parameters.

f_(t), i_(t), o_(t) ∈

^(d) are called forget, input, output gates, respectively, and theirvalues are in the range of [0,1]. These gates control how muchinformation to keep/throw away.

σ(⋅), ⊕ and ⊙ represent an element-wise sigmoid function, concatenationoperator, and an element-wise multiplication, respectively. The LSTMunit can be rewritten as follows, where θ represents all the parameters.

(h _(t) ,c _(t))=LSTM(h _(t−1) ,c _(t−1) ,x _(t),θ)

The exemplary method can take the concatenation of the duration l_(k)^(i) and slope s_(k) ^(i) as the input data x_(k) ^(i), and feed thisconcatenation in each trend of all time series into LSTM to learn thelong-term trend dependency. After feeding the trend sequence

into LSTM, the hidden state h_(t) at the last time step is used as theoverall representation of the trend sequences.

Individual time series usually present different dynamics. However, asthe basic LSTM blindly blends the information of all time series intothe hidden state h_(t), it is intractable to further learn the timeseries-specific representations. Besides, the relatedness among thetrend learning tasks of different time series cannot be modeled by thehidden state mixing multivariate data, thus potentially hurting thetrend learning task performance.

The exemplary methods tensorize the hidden states to learn the timeseries specific representation, such that the hidden representation ofeach time series can be learned exclusively based on the data from thattime series.

The intuition behind tensorizing hidden states is that the exemplarymethod a represents the hidden state as a matrix H_(t)=(h_(t) ¹, . . . ,h_(t) ^(n))^(T), where h_(t) ^(i) ∈

^(d) ⁰ is the hidden state vector specific to the ith time series. Thedata used to generate h_(t) ^(i) is exclusively related to the i-th timeseries.

Given the newly coming data x_(t)∈

^(n) and the previous state matrix H_(t−1), the hidden state is updatedas follows:

{tilde over (C)} _(t)=tan h(W _(c)

x _(t) +u _(c)└_(n) H _(t−1) +B _(c))

where {tilde over (C)}_(t)=({tilde over (c)}_(t) ¹, . . . , {tilde over(c)}_(t) ^(n))^(T) has the same shape of the hidden state matrixH_(t−1). The element {tilde over (c)}_(t) ^(i)∈

^(d) ⁰ corresponds to the hidden state update of the i-th time series.

W_(c)=w_(c) ¹, . . . , w_(c) ^(n))^(T)∈

^(n×d) ⁰ is the input-to-hidden transition matrix, where w_(c) ^(i)∈

^(d) ⁰ . W_(c)

x_(t) captures the information from the input data and is defined by:

W _(c)

x _(t)=(w _(x) ¹ x _(t) ¹ , . . . ,w _(x) ^(n) x _(t) ^(n))^(T).

u_(c)=(U_(c) ¹, . . . , U_(c) ^(n))^(T) ∈

^(n×d) ⁰ ^(×d) ⁰ is the hidden-to-hidden transition tensor, where U_(c)^(i)∈

^(d) ⁰ ^(×d) ⁰ . u_(c)⊗_(n)H_(t−1) captures the information from theprevious state matrix:

u _(c)⊗_(n) H _(t−1)=(U _(c) ¹ h _(t−1) ¹ , . . . ,U _(h) ^(n) h _(t−1)^(n))^(T)

where ⊗_(n) indicates the tensor product along the axis of n.

From an MTL viewpoint, tensorizing hidden states transform the hiddenstate update of multivariate time series into multiple independenttasks, each of which corresponds to a time series. Thus, MTL helpslearning time series-specific representations. However, MTL cannot modelthe task relatedness.

The exemplary methods introduce an adaptive shared memory to model taskrelatedness. The goal is to make more related tasks share more modelarchitecture/parameters and less related ones share less.

FIGS. 7-8 illustrate the architecture of TLASM 700A-700B, in which thecells 701, 703, 711, 713, are task-specific units and the centralcomponents are the adaptive shared memory that includes multiple layersof parallel sub-networks. In the adaptive shared memory module, thefirst layer includes multiple independent LSTMs 705, 715, followed byseveral sub-networks 707, 717 including multiple multilayer perceptrons(MLPs). The last layer 709, 719 is task specific MLPs employed tocollect information for specific tasks 405 (FIG. 4). The connectionbetween the sub-networks is a weighted average with attention mechanism.All the independent LSTMs and subnetworks are shared by all predictiontasks. The adaptive shared memory learns the connections between thesubnetworks to encode the architecture space, which generates differentsub-network routings. The adaptive shared memory achieves a flexibleparameter sharing by learning to select a similar sub network routingfor related tasks. Besides, because the adaptive shared memory includesLSTMs as the first layer to read information from time series at eachtime step, the adaptive shared memory is able to model the taskrelatedness that may change over time.

The intuition behind multiple LSTMs included in the adaptive sharedmemory is that there are different shared hidden feature spaces for thetasks and each LSTM corresponds to one of them. Suppose the 1 layerincludes p standard LSTMs and the 2nd layer includes q MLPs. Afterfeeding all the trend sequence data into these LSTMs, the outputs attime step t are:

(h _(t) ⁽¹⁾ ,c _(t) ⁽¹⁾)=LSTM₁(h _(t−1) ⁽¹⁾ ,c _(t−1) ⁽¹⁾ ,x _(t),θ⁽¹⁾)

. . .

(h _(t) ^((p)) ,c _(t) ^((p)))=LSTM_(p)(h _(t−1) ^((p)) ,c _(t−1) ^((p)),x _(t),θ^((p))).

For the sub-network routing between the 1^(st) layer and the 2^(nd)layer, the exemplary methods use a weighted average of the 1^(st)layer's outputs:

${\begin{bmatrix}e_{1} \\e_{2} \\\vdots \\e_{q}\end{bmatrix} = {\begin{bmatrix}{\alpha_{11}I_{11}} & \cdots & {\alpha_{1p}I_{1p}} \\\vdots & \ddots & \vdots \\{\alpha_{q\; 1}I_{q\; 1}} & \cdots & {\alpha_{qp}I_{qp}}\end{bmatrix}\begin{bmatrix}h_{t}^{(1)} \\h_{t}^{(2)} \\\vdots \\h_{t}^{(p)}\end{bmatrix}}},$

where α_(ij)≥0 is the weight, Σ_(j)α_(ij)=1 and I_(ij) is the identitymatrix. α_(ij) represents the degree of connection between sub-networksand is learned by an attention module:

${\alpha_{ij} = \frac{\exp \left\{ {w_{i}^{\top}\mspace{14mu} {\tanh \left( {V_{i}h_{t}^{(j)}} \right)}} \right\}}{\sum\limits_{k = 1}^{q}\; {\exp \left\{ {w_{i}^{\top}\mspace{14mu} {\tanh \left( {V_{i}h_{t}^{(k)}} \right)}} \right\}}}},$

where w_(i)∈

^(d) ^(α) and V^(i)∈

^(d) ^(α) ^(×d) are parameters. The number of attentions used betweentwo layers equals to the number of sub-networks in the latter layer.Similarly, the sub-network routing between other layers is designed. Theattentions between different layers are different. As the number ofsubnetworks in the final layer equals to the number of tasks, e.g., thenumber of time series, the exemplary method can get the output of thelast layer as R_(t)=(r_(t) ¹, . . . , r_(t) ^(n))^(T), where r_(t) ^(i)∈

^(d) ^(r) is the information read from the shared memory for the i-thtime series.

With the tensorized hidden states mechanism and the adaptive sharedmemory, the exemplary method employs TLASM. The intuition behind TLASMis that the hidden state of time series is influenced by both theinformation from that time series and the information from related ones.Specifically, each time series has its own memory c_(t) ^(i)∈

^(d) ⁰ storing the time series-specific information and the adaptiveshared memory r_(t) ^(i)∈

^(d) ^(r) storing the information of related time series. Whengenerating the hidden state of the i-th time series h_(t) ^(i), it needsto read information from both the two memories r_(t) ^(i) and c_(t)^(i).

The calculation process of the TLASM unit is described in the equationsbelow. As a standard LSTM neural network, TLASM has the forget gateF_(t), input gate I_(t), output gate O_(t) and the memory cell C_(t) inthe update process.

Given the input data x₁, x₂, . . . ∈

^(n), the cell matrix C_(t) and the state matrix H_(t) are calculated asfollows:

${\begin{bmatrix}F_{t} \\I_{t} \\O_{t}\end{bmatrix} = {\begin{bmatrix}\sigma \\\sigma \\\sigma\end{bmatrix}\left( {{W\mspace{14mu} \mspace{14mu} x_{t}} + {U \otimes_{n}H_{t - 1}} + B} \right)}},{C_{t} = {{F_{t} \odot C_{t - 1}} + {I_{t} \odot {\overset{\sim}{C}}_{t}}}},{G_{t} = {\sigma \left( {{U_{c} \otimes_{n}C_{t}} + {U_{r} \otimes_{n}R_{t}}} \right)}},{H_{t} = {O_{t} \odot {\tanh \left( {C_{t} + {G_{t} \odot \left( {U_{g} \otimes_{n}R_{t}} \right)}} \right)}}},$

where W∈

^(3n×d) ⁰ , u∈

^(3n×d) ⁰ ^(×d) ⁰ , B∈

^(3n×d) ⁰ , and u_(c), u_(r), u_(g)∈

^(n×d) ⁰ ^(×d) ⁰ are parameters. {tilde over (C)}_(t) is the updatedstate matrix.

F_(t), I_(t), O_(t)∈

^(n×d) are the gates in the form of matrix.

G_(t)∈

^(n×d) is a fusion gate. The fusion gate selects a part of theinformation read from the shared memory, which is merged with the timeseries-specific memory into a new one for each task.

Similar to the case of tensorizing hidden states, the tensor-dotoperations ensure the data used to generate the gates and the memorycell matrix of each time series are exclusively from the correspondingtime series. TLASM can also be considered as a set of parallel LSTMs,each of which processes one time series and then merges via the adaptiveshared memory.

Regarding the deep architecture with TLASM for learning trends inmultivariate time series, the overview of the deep architecture is shownin FIG. 4. The sequences of historical trends of all time series are fedinto TLASM 401 to learn the long-term trend evolving. A multi-task 1dCNN403 is applied to the local raw data of each time series to extractlocal features. The outputs of TLASM 401 and 1dCNN 403 are further fedinto a task-specific subnetwork to get the final trend prediction ofthat time series.

Regarding TLASM for learning long-term trend evolving, the trendsequences of all time series, e.g.,

={

l_(k) ¹,s_(k) ¹

}∪ . . . ∪{

l_(k) ^(n),s_(k) ^(n)

}, are fed into TLASM to learn long-term trend evolving. Specifically,the exemplary methods concatenate l and s of all time series as theinput data x_(t)=(l_(t) ¹, s_(t) ¹, . . . , l_(t) ^(n), s_(t) ^(n))^(T)∈

^(2n). The output of TLASM, H∈

^(2n×d), is the transformed representation of all trend sequences. Theexemplary method denotes L^(i)(

) as the part of H that corresponds to the i-th time series

Regarding multi-task 1dCNN for learning local features, to extract thefeatures of local time series data, DeepTrends 400 employs a multi-task1CNN module which enjoys the classic architecture of the shared bottomMTL. In the module, a low-level subnetwork is shared by all time seriesand each time series has its own subnetwork built on top of the sharedone. All these subnetworks include multiple stacked layers of idconvolutional, activation and pooling operations. The elements of localdata

={

x_(t) _(k) _(−w) ¹, . . . , x_(t) _(k) ¹

}∪ . . . ∪{

x_(t) _(k) _(−w) ^(n), . . . , x_(t) _(k) ^(n)

} are fed into the multi-task 1dCNN module. The output that correspondsto the i-th time series is denoted by C^(i)(

).

Regarding task-specific sub-networks, the exemplary methods design atask-specific sub-network for the trend learning of each time series.The outputs of TLASM and multi-task 1dCNN, e.g., L^(i)(

) and C^(i)(

), are concatenated and fed into the task-specific sub-network. Theoutput of the sub-network for the i-th time series is:

{circumflex over (l)} ^(i) ,ŝ ^(i)

=f ^(i)(L ^(i)(

)⊗C ^(i)(

)),

where f^(i)(⋅) represents an MLP that includes of m layers of neurons.The output of the k-th layer can be expressed as y_(k)=φ(W_(k)^(i)(y_(k−1))+b_(k) ^(i)), where φ is the leaky ReLU activation functionand W_(k) ^(i), b_(k) ^(i) are parameters.

Regarding the objective function, given the trend sequences

and the local data

, the objective function is:

${J = {{\frac{1}{n}{\sum\limits_{i = 1}^{n}\; {\frac{1}{z^{i}}{\sum\limits_{k = 1}^{z^{i}}\; \left\lbrack {\left( {{\hat{l}}_{k}^{i} - l_{k}^{i}} \right)^{2} + \left( {{\hat{s}}_{k}^{i} - s_{k}^{i}} \right)^{2}} \right\rbrack}}}} + {\lambda \; P_{nn}}}},$

where z^(i) is the number of trends in the i-th time series and P_(nn)is the penalization term for the parameters to prevent the model fromover-fitting. λ is a hyper-parameter.

In summary, the exemplary embodiments introduce a deep architecture,DeepTrends, for learning trends in multivariate time series. The coremodule of DeepTrends is a TLASM network, which is used to capture thelong-term dependency in the historical trend sequence. Particularly,TLASM tensorizes the hidden states to model the complex temporalpatterns in different tasks. An adaptive shared memory is introduced tolearn the task relatedness and dynamically integrates the sharedinformation from related tasks into the learning process of individualtasks. To consider the short-term dependency between the local data andthe subsequent trend, a multi-task 1dCNN is designed to extract thefeatures of local raw time series. A task-specific sub-network isfurther designed to integrate the long- and short-term dependency.

FIG. 9 is block/flow diagram of an exemplary processing system forunsupervised multivariate time series trend detection for group behavioranalysis, in accordance with embodiments of the present invention.

The processing system includes at least one processor or processordevice (CPU) 904 and a graphics processing unit (GPU) 905 operativelycoupled to other components via a system bus 902. A cache 906, a ReadOnly Memory (ROM) 908, a Random Access Memory (RAM) 910, an input/output(I/O) adapter 920, a network adapter 930, a user interface adapter 940,and a display adapter 950, are operatively coupled to the system bus902. Sensors for collecting time series data 960 can be employed via thebus 602. The time series data can be analyzed with the TLASM 970.

A storage device 922 is operatively coupled to system bus 902 by the I/Oadapter 920. The storage device 922 can be any of a disk storage device(e.g., a magnetic or optical disk storage device), a solid statemagnetic device, and so forth.

A transceiver 932 is operatively coupled to system bus 902 by networkadapter 930.

User input devices 942 are operatively coupled to system bus 902 by userinterface adapter 940. The user input devices 942 can be any of akeyboard, a mouse, a keypad, an image capture device, a motion sensingdevice, a microphone, a device incorporating the functionality of atleast two of the preceding devices, and so forth. Of course, other typesof input devices can also be used, while maintaining the spirit of thepresent invention. The user input devices 942 can be the same type ofuser input device or different types of user input devices. The userinput devices 942 are used to input and output information to and fromthe processing system.

A display device 952 is operatively coupled to system bus 902 by displayadapter 950.

Of course, the processing system may also include other elements (notshown), as readily contemplated by one of skill in the art, as well asomit certain elements. For example, various other input devices and/oroutput devices can be included in the system, depending upon theparticular implementation of the same, as readily understood by one ofordinary skill in the art. For example, various types of wireless and/orwired input and/or output devices can be used. Moreover, additionalprocessors, processor devices, controllers, memories, and so forth, invarious configurations can also be utilized as readily appreciated byone of ordinary skill in the art. These and other variations of theprocessing system are readily contemplated by one of ordinary skill inthe art given the teachings of the present invention provided herein.

FIG. 10 is a block/flow diagram of an exemplary method for unsupervisedmultivariate time series trend detection for group behavior analysis, inaccordance with embodiments of the present invention.

At block 1001, collect multi-variate time series data from a pluralityof sensors.

At block 1003, learn piecewise linear trends jointly for all of themulti-variate time series data.

At block 1005, divide the multi-variate time series data into aplurality of time segments.

At block 1007, count a number of up/down trends in each of the pluralityof time segments.

At block 1009, for a training phase, employ a cumulative sum (CUSUM).

At block 1011, for a testing phase, monitor the CUSUM for trend changes.

FIG. 11 is a block/flow diagram of equations employed in methods forunsupervised multivariate time series trend detection for group behavioranalysis, in accordance with embodiments of the present invention.

Equations 1100 identify a learning piecewise linear trends for all timeseries jointly, a CUSUM, an attention module, and an objective function.

FIG. 12 is a block/flow diagram of practical applications forunsupervised multivariate time series trend detection for group behavioranalysis, in accordance with embodiments of the present invention.

Practical applications for learning and forecasting trends inmultivariate time series data can include, but are not limited to,system monitoring 1201, healthcare 1203, stock market data 1205,financial fraud 1207, gas detection 1209, and e-commerce 1211. Thetime-series data in such practical applications can be collected bysensors 1500 (FIG. 15).

FIG. 13 is a block/flow diagram of method for tensorized LSTM withadaptive shared memory for learning trends in multivariate time series,in accordance with embodiments of the present invention.

At block 101, a multi-variate time series is input.

At block 103, joint piecewise linear trends are learned.

At block 1301, the TLASM model is trained using historical trendsequences and local time series.

At block 1303, the future trend's slope and length are predicted.

FIG. 14 are block/flow diagrams of training the TLASM model andpredicting future trend's slope and length, in accordance withembodiments of the present invention.

At block 1401, the TLASM model is trained using historical trendsequences and local time series.

At block 1411, the framework in FIG. 4 is employed to train theprediction model.

At block 1413, the model uses 1dCNN to learn the local short-term timeseries patterns and tensorized LSTM with adaptive shared memory forlearning long-term trend sequences.

At block 1403, the future trend's slope and length are predicted.

At block 1421, the prediction feeds the learned model and recent trendsequences and most recent short-term raw time series to predict nearfuture trend of each time series.

At block 1423, the learning procedure is by nature a multi-task way.

FIG. 15 is a block/flow diagram of exemplary IoT sensors used to collectdata/information for unsupervised multivariate time series trenddetection for group behavior analysis, in accordance with embodiments ofthe present invention.

IoT loses its distinction without sensors. IoT sensors act as defininginstruments which transform IoT from a standard passive network ofdevices into an active system capable of real-world integration.

The IoT sensors 1500 can be connected via the mobile networks 1550 totransmit information/data, continuously and in in real-time. ExemplaryIoT sensors 1500 can include, but are not limited to,position/presence/proximity sensors 1501, motion/velocity sensors 1503,displacement sensors 1505, such as acceleration/tilt sensors 1506,temperature sensors 1507, humidity/moisture sensors 1509, as well asflow sensors 1510, acoustic/sound/vibration sensors 1511, chemical/gassensors 1513, force/load/torque/strain/pressure sensors 1515, and/orelectric/magnetic sensors 1517. One skilled in the art can contemplateusing any combination of such sensors to collect data/information andinput into the TLASM model 1560 of the mobile networks 1550 for furtherprocessing. One skilled in the art can contemplate using other types ofIoT sensors, such as, but not limited to, magnetometers, gyroscopes,image sensors, light sensors, radio frequency identification (RFID)sensors, and/or micro flow sensors. IoT sensors can also include energymodules, power management modules, RF modules, and sensing modules. RFmodules manage communications through their signal processing, WiFi,ZigBee®, Bluetooth®, radio transceiver, duplexer, etc.

Moreover data collection software can be used to manage sensing,measurements, light data filtering, light data security, and aggregationof data. Data collection software uses certain protocols to aid IoTsensors in connecting with real-time, machine-to-machine networks. Thenthe data collection software collects data from multiple devices anddistributes it in accordance with settings. Data collection softwarealso works in reverse by distributing data over devices. The system caneventually transmit all collected data to, e.g., a central server.

FIG. 16 is a block/flow diagram of an exemplary method for tensorizedLSTM with adaptive shared memory for learning trends in multivariatetime series, in accordance with embodiments of the present invention.

At block 1601, collect multi-variate time series data from a pluralityof sensors

At block 1603, jointly learn both local and global contextual featuresfor predicting a trend of the multivariate time series by employing atensorized long short-term memory (LSTM) with adaptive shared memory(TLASM) to learn historical dependency of historical trends.

At block 1605, employ a multi-task one-dimensional convolutional neuralnetwork (1dCNN) to extract salient features from local raw time seriesdata to model a short-term dependency between local time series data andsubsequent trends.

As used herein, the terms “data,” “content,” “information” and similarterms can be used interchangeably to refer to data capable of beingcaptured, transmitted, received, displayed and/or stored in accordancewith various example embodiments. Thus, use of any such terms should notbe taken to limit the spirit and scope of the disclosure. Further, wherea computing device is described herein to receive data from anothercomputing device, the data can be received directly from the anothercomputing device or can be received indirectly via one or moreintermediary computing devices, such as, for example, one or moreservers, relays, routers, network access points, base stations, and/orthe like. Similarly, where a computing device is described herein tosend data to another computing device, the data can be sent directly tothe another computing device or can be sent indirectly via one or moreintermediary computing devices, such as, for example, one or moreservers, relays, routers, network access points, base stations, and/orthe like.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module,” “calculator,”“device,” or “system.” Furthermore, aspects of the present invention maytake the form of a computer program product embodied in one or morecomputer readable medium(s) having computer readable program codeembodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical datastorage device, a magnetic data storage device, or any suitablecombination of the foregoing. In the context of this document, acomputer readable storage medium may be any tangible medium that caninclude, or store a program for use by or in connection with aninstruction execution system, apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server.

In the latter scenario, the remote computer may be connected to theuser's computer through any type of network, including a local areanetwork (LAN) or a wide area network (WAN), or the connection may bemade to an external computer (for example, through the Internet using anInternet Service Provider).

Aspects of the present invention are described below with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of thepresent invention. It will be understood that each block of theflowchart illustrations and/or block diagrams, and combinations ofblocks in the flowchart illustrations and/or block diagrams, can beimplemented by computer program instructions. These computer programinstructions may be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create means for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks or modules.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks or modules.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks or modules.

It is to be appreciated that the term “processor” as used herein isintended to include any processing device, such as, for example, onethat includes a CPU (central processing unit) and/or other processingcircuitry. It is also to be understood that the term “processor” mayrefer to more than one processing device and that various elementsassociated with a processing device may be shared by other processingdevices.

The term “memory” as used herein is intended to include memoryassociated with a processor or CPU, such as, for example, RAM, ROM, afixed memory device (e.g., hard drive), a removable memory device (e.g.,diskette), flash memory, etc. Such memory may be considered a computerreadable storage medium.

In addition, the phrase “input/output devices” or “I/O devices” as usedherein is intended to include, for example, one or more input devices(e.g., keyboard, mouse, scanner, etc.) for entering data to theprocessing unit, and/or one or more output devices (e.g., speaker,display, printer, etc.) for presenting results associated with theprocessing unit.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that theembodiments shown and described herein are only illustrative of theprinciples of the present invention and that those skilled in the artmay implement various modifications without departing from the scope andspirit of the invention. Those skilled in the art could implementvarious other feature combinations without departing from the scope andspirit of the invention. Having thus described aspects of the invention,with the details and particularity required by the patent laws, what isclaimed and desired protected by Letters Patent is set forth in theappended claims.

What is claimed is:
 1. A computer-implemented method executed on aprocessor for unsupervised multivariate time series trend detection forgroup behavior analysis, the method comprising: collecting multi-variatetime series data from a plurality of sensors; learning piecewise lineartrends jointly for all of the multi-variate time series data; dividingthe multi-variate time series data into a plurality of time segments;counting a number of up/down trends in each of the plurality of timesegments; for a training phase, employing a cumulative sum (CUSUM); andfor a testing phase, monitoring the CUSUM for trend changes.
 2. Themethod of claim 1, wherein the learning of the piecewise linear trendsinvolves using: ∑ t = 1 T    y ^ t - x ^ t  2 2 + λ  ∑ t = 2 T - 1   x ^ t - 1 - 2  x ^ t + x ^ t + 1  2 , where   y ^ t , x ^ t ∈k and where y_(t) is original multi-variate time series values at timestep t, which is a k-dimensional vector (R^(k×1)), x_(t) is an estimatedvalue to be optimized, and λ is used to control a granularity of theinferred trends.
 3. The method of claim 2, wherein the first term is aresidual term and the second term is a smoothness term.
 4. The method ofclaim 3, wherein if λ is above a predetermined threshold, a resultingtrend is coarse grained.
 5. The method of claim 1, wherein, when theCUSUM is larger than a predetermined threshold, a group of themulti-variate time series data has an upward trend.
 6. The method ofclaim 1, wherein when the CUSUM is less than a predetermined threshold,a group of the multi-variate time series data has a downward trend. 7.The method of claim 1, wherein the CUSUM is given as:${S_{n} = {\sum\limits_{i = 1}^{n}\; {\left( {z_{n} - \mu} \right)\text{/}\sigma_{z}}}},$where μ is a mean value of z in a training period, σ_(z) is a standarderror of z in the training period, and z_(n) is a number of uptrends. 8.A non-transitory computer-readable storage medium comprising acomputer-readable program for unsupervised multivariate time seriestrend detection for group behavior analysis, wherein thecomputer-readable program when executed on a computer causes thecomputer to perform the steps of: collecting multi-variate time seriesdata from a plurality of sensors; learning piecewise linear trendsjointly for all of the multi-variate time series data; dividing themulti-variate time series data into a plurality of time segments;counting a number of up/down trends in each of the plurality of timesegments; for a training phase, employing a cumulative sum (CUSUM); andfor a testing phase, monitoring the CUSUM for trend changes.
 9. Thenon-transitory computer-readable storage medium of claim 8, wherein thelearning of the piecewise linear trends involves using: ∑ t = 1 T   y ^ t - x ^ t  2 2 + λ  ∑ t = 2 T - 1    x ^ t - 1 - 2  x ^ t + x^ t + 1  2 , where   y ^ t , x ^ t ∈ k and where y_(t) is originalmulti-variate time series values at time step t, which is ak-dimensional vector (R^(k×1)), x_(t) is an estimated value to beoptimized, and λ is used to control a granularity of the inferredtrends.
 10. The non-transitory computer-readable storage medium of claim9, wherein the first term is a residual term and the second term is asmoothness term.
 11. The non-transitory computer-readable storage mediumof claim 10, wherein if λ is above a predetermined threshold, aresulting trend is coarse grained.
 12. The non-transitorycomputer-readable storage medium of claim 8, wherein, when the CUSUM islarger than a predetermined threshold, a group of the multi-variate timeseries data has an upward trend.
 13. The non-transitorycomputer-readable storage medium of claim 8, wherein when the CUSUM isless than a predetermined threshold, a group of the multi-variate timeseries data has a downward trend.
 14. The non-transitorycomputer-readable storage medium of claim 8, wherein the CUSUM is givenas:${S_{n} = {\sum\limits_{i = 1}^{n}\; {\left( {z_{n} - \mu} \right)\text{/}\sigma_{z}}}},$where μ is a mean value of z in a training period, σ_(z) is a standarderror of z in the training period, and z_(n) is a number of uptrends.15. A system for unsupervised multivariate time series trend detectionfor group behavior analysis, the system comprising: a memory; and one ormore processors in communication with the memory configured to: collectmulti-variate time series data from a plurality of sensors; learnpiecewise linear trends jointly for all of the multi-variate time seriesdata; divide the multi-variate time series data into a plurality of timesegments; count a number of up/down trends in each of the plurality oftime segments; for a training phase, employ a cumulative sum (CUSUM);and for a testing phase, monitor the CUSUM for trend changes.
 16. Thesystem of claim 15, wherein the learning of the piecewise linear trendsinvolves using: ∑ t = 1 T    y ^ t - x ^ t  2 2 + λ  ∑ t = 2 T - 1   x ^ t - 1 - 2  x ^ t + x ^ t + 1  2 , where   y ^ t , x ^ t ∈k and where y_(t) is original multi-variate time series values at timestep t, which is a k-dimensional vector (R^(k×1)), x_(t) is an estimatedvalue to be optimized, and λ is used to control a granularity of theinferred trends.
 17. The system of claim 16, wherein the first term is aresidual term and the second term is a smoothness term.
 18. The systemof claim 17, wherein if λ is above a predetermined threshold, aresulting trend is coarse grained.
 19. The system of claim 15, wherein,when the CUSUM is larger than a predetermined threshold, a group of themulti-variate time series data has an upward trend.
 20. The system ofclaim 15, wherein when the CUSUM is less than a predetermined threshold,a group of the multi-variate time series data has a downward trend.